Order of integers and primitive roots

Let a,m be in Z with m>0. If a' is the inverse of a modulo m, prove that the order of a modulo m is equal to the order of a' modulo m. Deduce that if r is a primitive root modulo m, then r' is a primitive root modulo m.

Let a,m be in Z with m>0. If a' is the inverse of a modulo m, prove that the order of a modulo m is equal to the order of a' modulo m. Deduce that if r is a primitive root modulo m, then r' is a primitive root modulo m.

The first part as Tinyboss noted follows easily from consider elements of